Question

I thought of a number, divided it by 1 1/2 , then added 2 1/2 to the result, then multiplied the sum by 1 2/3 . Then I subtracted 1 2/3 and got the result 2 5/6 . What was my number?

Answer 1

Answer: The number is $\dfrac3{10}$ or 0.3.

Step-by-step explanation:

Let x be the number.

Then,

$((x\div 1\dfrac12)+2\dfrac12)\times1\dfrac23-1\dfrac23=2\dfrac56$

First simplify each mixed fraction into improper fraction, we get

$((x\div \dfrac32)+\dfrac52)\times\dfrac53-\dfrac53=\dfrac{17}6\\\\\text{Now, }((x\div \dfrac32)+\dfrac52)\times\dfrac53=\dfrac{17}{6}+\dfrac53\\\\\Rightarrow\ ((x\div \dfrac32)+\dfrac52)\times\dfrac53=\dfrac92\\\\\Rightarrow\ ((x\div \dfrac32)+\dfrac52)=\dfrac92\times\dfrac35\\\\\Rightarrow\ ((x\div \dfrac32)+\dfrac52)=\dfrac{27}{10}\\\\\Rightarrow\ (x\div \dfrac32)=\dfrac{27}{10}-\dfrac52\\\\\Rightarrow\ (x\div \dfrac32)=\dfrac2{10}\\\\\Rightarrow\ x=\dfrac2{10}\times\dfrac32\\\\\Rightarrow\ x=\dfrac3{10}$

Hence, the number is $\dfrac3{10}$ or 0.3.